Anderson LocalizationDrop a quantum wave onto a perfectly even row of atomic sites and it spreads out forever, a widening cone rippling both ways. Make the row uneven — scatter each site's energy at random — and the very same wave spreads for a moment, then simply stops and sits frozen in place, forever, going nowhere.Philip Anderson found in 1958 that in one dimension any amount of disorder is enough: waves scattering off every random bump interfere with each other so thoroughly that they cancel out everywhere except an exponentially small patch near where they started. The clean lattice ships probability ballistically at up to twice the hopping rate; the disordered one traps it inside a localization length that shrinks as the disorder grows — the reason thin enough dirty wires are insulators even though every atom in them is a perfectly good conductor.